Mathematical Developments in Modelling Microstructure and Phase Transformations in Solids

6-18 and 20-24 September 1999

The Summer School and Concentration will kick-off the programme Mathematical Developments in Solid Mechanics and Materials Science. The recent years have seen much advance in the mathematical aspects of materials science and solid mechanics. Materials science and solid mechanics have posed interesting questions in mathematics and in turn mathematical analysis has brought new insights in these areas. The key issue is how the microscopic structure of a solid material influences its macroscopic response to stimuli like stress and magnetic field, and conversely how the application of macroscopic loads influences the microstructure. In particular, phase transformations, damage and fracture may occur, creating structures at various length scales which can evolve with macroscopic stimulus. The challenge, both for mathematics and physical modelling, is to comprehend relationships between models at different length scales. This has led already to well-developed theories in static or equilibrium situations. Length scales can be linked using the theory of ``homogenization'' when the scales are widely separated, and the formation of microstructure can be addressed using a class of variational problems that do not admit classical solutions, but only those which are highly oscillatory. Mathematical tools for describing microstructure have been developed and these have been used to study the link between microstructure and macroscopic properties. Yet challenges remain, and these have inspired different approaches. Much of this development has been at the continuum level and linking it to the atomistic length scales is a continuing theme. Some phenomena may be unstable, at least at the microscopic level, and, even if stable, may admit multiple equilibria. Therefore, the study of the kinetics of the processes is a key requirement, making demands for modelling, for computation and for the analysis of partial differential equations. In particular, the (possibly hierarchical) development of large-scale patterns is an important challenge.

The EC summer school will be for two weeks, 6-18 September 1999. The first week consists of four sets of expository lectures by

G Allaire (Paris VI)

Homogenization and Applications to Materials Science

M Finnis (Belfast)

Atomistic Models

S Müller (MPI, Leipzig)

Mathematics of Microstructure

E Van der Giessen (Delft)

Damage and Fracture Mechanics

The second week surveys the latest developments and the speakers are expected to include

R Abeyaratne (MIT)

J M Ball (Oxford)

M Berveiller (Metz)

H Bhadeshia (Cambridge)

K Bhattacharya (Caltech)

L-Q Chen (Penn State)

A DeSimone (MPI Leipzig)

L B Freund (Brown)

G Friesecke (Oxford)

R D James (Minnesota)

D Kinderlehrer (CMU)

P Leo (Minnesota)

M Luskin (Minnesota)

V Nesi (Rome)

F Otto (UCSB)

K Rabe (Yale)

E Salje (Cambridge)

D Schryver (Antwerp)

B Spencer (SUNY Buffalo)

P Voorhees (Northwestern)

This will be followed by a concentration for a week, 20-24 September 1999, during which the speakers above and other experts will be in residence enabling less formal presentations, discussions and talks.

Limited funding is available for attending the EC Summer School to graduate and post-doctoral students who are citizens of European Community countries and are of age 35 or less.